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Critical Assessment of Downscaling Procedures in Climate Change Impact Models Zekâi S ¸ en I·stanbul Technical University, Civil Engineering Faculty, Hydraulics and Water Resources Division, Maslak 34469, Istanbul E-mail: [email protected] Received July 14, 2009, Revised August 28, 2009, Accepted August 28, 2009 Abstract General Circulation (Climate) Models (GCMs) from different research centers of the world provide future replicates of various meteorological variables up to years 2100 at rather coarse mesh nodes of about 250 km apart from each other. These models are based on the physically dynamic equations of energy, momentum and mass conservation in addition to the state equation of gases. Hence, an arena of equations requires simultaneous solution by considering global initial and boundary conditions. It is necessary to downscale the GCM results at coarse nodes to locally smaller scales so as to match the historical data sequences to scenario series. Such downscaling procedures are necessary for climate change impact effect assessments including vulnerability, mitigation and adaptation works at finer scales. Various methods have been suggested so far in the literature for downscaling and still new ones are expected to come in the future. It is the main purpose of this paper to provide the critical review of available methods and then to suggest a regional dependence function based on the point cumulative semivariogram technique. Keywords: Dependence function, downscaling, dynamic, general circulation, hybrid, model, precipitation, spatial, statistics. INTRODUCTION During the last three decades terms ‘global change’, ‘global warming’, ‘greenhouse effect’, and ‘climate change’ are coined in such a manner that almost every country, society, establishment and even individual became interested in their impacts. Unfortunately, many mismanagement procedures and their consequences on the environment in terms of water shortages, electricity generation (fossil and renewable sources), food security and sea level rise are counted among the causes of climate change. Even there are disagreements about the climate change occurrence among the scientists but IPCC (2007) report help for a better consensus on this topic with at least a fuzzy conviction in every scientist. Tripathi et al (2006) recently have presented a detailed literature review. The evidence of climatic link with hydrology of fresh water resources (IPCC, 2007, Kundzewicz et al, 2007, 2008) necessitates development of effective strategies for regional hydrologic analysis to cope with critical water shortages in the future. To progress towards this goal, it is necessary to develop an efficient downscaling strategy to interpret climate change signals at regional scale. The recent scientific evidence that the climate is changing and will continue to change for many years necessitates improvement in our understanding of the global climate system in order to assess the possible impact of a climate change on various sectors and especially on the hydrological cycle and water resources. Climate change scenarios are supported by General Circulation Models (GCMs), which describe dynamically the atmospheric and coupled oceanographic processes by mathematical equations. The resolution of the current GCMs is coarser than 2°, which is of the order of a few hundred kilometers between grid points. Contrary to coarse scale human activities the assessment of climate change impact requires finer scales at the order of a several kilometers. Hence, there is a mismatch between the GCM

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scenario outputs and the practically applicable scales on the earth’s surface. This mismatch has led to development of several downscaling methodologies, which have been applied for different purposes such as for scenario construction, simulation and prediction of meteorological variables including temperature, precipitation, humidity, solar irradiation, wind speed in addition to many others as indicated in the following list. 1) 2)

Regional precipitation for water resources works (Kim et al., 2004; S ¸ en, 2009), Low-frequency rainfall eventsfor drought duration, magnitude, andintensity assessments (Wilby, 1998), 3) Mean, minimum and maximum air temperatures for various agricultural patterns and energy requirements (Kettle and Thompson, 2004), 4) Soil moisture for irrigation studies and agriculture (Georgakakos and Smith, 2001; Jasper et al., 2004), 5) Runoff for flood predictions (Arnell et al., 2003) and streamflows for various risk calculations (Cannon and Whitfield, 2002), 6) Ground water levels for water abstraction and recharge possibilities (Bouraoui et al., 1999), 7) Transpiration for plant water use (Misson et al., 2002), 8) Wind speed for evaporation and wind energy assessments (Faucher et al., 1999), 9) Potential evaporation rates (Weisse and Oestreicher, 2001), 10) Soil erosion and crop yield fo sedimentation and vegetation (Zhang et al., 2004), 11) Landslide occurrence for land use (Buma and Dehn, 2000; Schmidt and Glade, 2003), 12) Water quality for public health care (Hassan et al., 1998). In general, there are two downscaling procedures as dynamic and statistical approaches but they can also be combined to create a hybrid procedure. In all the previous studies the downscaling from GCMs results to finer scales could be classified broadly into three categories as follows. 1)

2)

Dynamic downscaling based on the conservation equations (mass, energy and momentum), planatery boundary conditions and state equation of gasses. In this approach, Regional Climate Model (RegCM) is embedded into a GCM. It is essentially a numerical model in which GCMs are used for the purpose of providing boundary conditions. Statistical downscaling based on multiple regression, stochastic modeling and various artificial intelligent methodologies. It has empirical relationships for transforming large-scale GCM features to finer scale regional variables such as temperature, precipitation, humidity, wind speed, solar irradiation and streamflow. Statistical downscaling is popular in the literature because its computational overhead is almost insignificant compared to dynamic downscaling. However, developing a statistical downscaling model for finer time scales (such as daily or hourly) often becomes a challenging task due to high memory requirements and slow convergence associated with modeling large data sets. Different versions of the statistical downscaling procedures are available such as Artificial Neural Network (ANN) techniques, and have gained wide recognition due to their ability to capture non-linear relationships between predictors (GCM scenario output data) and predictand (meteorological or hydrological data of interest in practice). Many researchers have worked with ANN and still new ones appear continuously in many scientific journals (Cavazos, 1997; Crane and Hewitson, 1998; Wilby et al., 1998; Trigo and Palutikof, 1999; Sailor et al., 2000; Snell et al., 2000; Mpelasoka et al., 2001; Schoof and Pryor, 2001; Cannon and Whitfield, 2002; Crane et al., 2002; Olsson et al., 2004; Shivam, 2004; Solecki and Oliveri, 2004; Tatli et al., 2004). Mathematically, an ANN has the ability to generalize a relationship from given patterns and it is possible for ANNs to model large-scale non-linear complex problems such as pattern recognition, and classification. Although there are many ANN technique applications in the literature, unfortunately, majority of them do not care about the physical, logical and rational bases behind the downscaling procedure. Along the similar line to statistical downscaling recently, Vapnik (1995, 1998) proposed a novel machine learning algorithm, which is also known as support vector machine (SVM).

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It provides an elegant solution to different problems including statistical downscaling and hence found wide application especially in the field of pattern recognition and time series analysis. Again numerous researchers used this approach for their problems among whom are Vapnik (1995, 1998), Cortes and Vapnik (1995), Scholkopf et al. (1998), Cristianini and Shawe-Taylor (2000), Haykin (2003) and Sastry (2003). It seems that the application of SVM approach to downscaling is computationally more intensive than the ANN method. However, this statistical downscaling technique is yet to find its way to downscaling applications and the comparison of its relative performance is still an open research issue. Several avenues should be explored to further refine this attempt to statistically downscale GCM simulations. A realistic simulation by GCM could yield pragmatic solution of predictand, while an inconsistent simulation could result in absurd values of the predictand. Hence, it is necessary to use simulations from more than one GCM for a given climate change scenario to test the robustness of the result projected by the downscaling model. The choice of predictor variables can significantly affect the result of a downscaling model. Since the climate variables affecting the precipitation vary across time and space, there is a need to identify/develop robust framework for selection of predictor variables in different parts of the world. Besides this, there are uncertainties associated with predictions of future climate change scenario and the assumption that the empirical relationships developed for the current state of atmosphere remain valid in the future. In spite of these uncertainties and assumptions downscaling remains the most popular tool for hydrologists to assess the impact of climate change on hydrological processes of a region (Tripathi et al, 2006). Hybrid downscaling, which is the mixture of the two previous downscaling procedures.

This paper touches on the problems and drawbacks with aforementioned downscaling procedures and suggests another version by considering the regional dependence function (RDF) concept for downscaling purpose. Although various statistical downscaling techniques have been used (Wilby and Wigley, 1997; Xu, 1999), such studies are not yet materialized in many parts of the world. In this paper, RDF based downscaling procedure is suggested for statistical downscaling of precipitation at monthly time scale from GCM scenario precipitation simulation generations. The effectiveness of the proposed approach is illustrated through its application to future climate projections. Nevertheless, it is worth mentioning that the future projections of hydrologic variables provided by a downscaling model for a given climate change scenario depend on the capability of GCM to simulate future climate. DOWNSCALING METHODS Downscaling is a method for obtaining high-resolution climate or climate change information. It is a transition process from relatively coarse-resolution GCMs, which have a resolution of 250–300 km by 250–300 km to finer (smaller) scales such as 50 km or less and even if possible at point scales, which is necessary to assess the impact of climate change at local levels. In general, there are three distinctive and at times and places complementary downscaling methods as dynamic downscaling (Figure 1), statistical downscaling (Figure 2) and hybrid downscaling (Figure 3), where P indicates pixel in the literature but point with the downscaling methodology presented later in this paper.

Downscaling

GCM

Figure 1. Dynamic downscaling


RegCM

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Downscaling

P

GCM

Figure 2. Statistical downscaling

Downscaling

GCM

Downscaling

P

RegCM

Figure 3. Hybrid downscaling

The (one-way) nested modeling technique has been increasingly applied to climate change studies in the last few years. This technique consists of using output from GCM simulations to provide initial and driving lateral meteorological boundary conditions for high-resolution RegCM simulations, with no feedback from the RegCM to the driving GCM. Hence, a regional increase in resolution can be attained through the use of nested RegCMs to account for sub-GCM grid-scale forcing. The most relevant advance in nested regional climate modeling activities was the production of continuous RegCM multi-year climate simulations. Previous regional climate change scenarios were mostly produced using samples of month-long simulations (IPCC 1996). The primary improvement represented by continuous long-term simulations consists of equilibration of model climate with surface hydrology and simulation of the full seasonal cycle for use in impact models. In addition, the capability of producing long-term runs facilitates the coupling of RegCMs to other regional process models, such as lake models, dynamical sea ice models, and possibly regional ocean (or coastal) and ecosystem models. The essence of statistical downscaling is first to derive statistical relationships between observed small-scale (often station, point level) variables and larger-scale GCM variables using various models. The initial step prior to any downscaling procedure is the downloading future values of the large-scale variables obtained from GCM projections and then their incorporation to drive the statistical relationships leading to the smaller-scale estimation of future climate patterns. Statistical downscaling is used whenever climate impact assessments are necessary and they require small-scale data. Especially, statistical downscaling is difficult to apply from first principles since it requires access to large data sets and considerable expertise to derive the relevant relationships. Among such downscaling techniques are, 1) 2)

Regional climate models, Weather classification and re-sampling,


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Mixtures of stochastic processes, weather generators, Linear and non–linear regression.

In order to achieve an effective downscaling procedure with reliable results the downscaling of GCM variables is sought to have the following features. 1) 2) 3) 4) 5)

High correlation with local variables, Physical and conceptual ideas must exist in the interpretation of the variable with relevant study area environment, It is necessary to maintain covariance and preferably the spatial dependence between local variables, GCM variables must be reliably available at a finite set of nodes around the study area, It must be possible to apply temporal downscaling and up-scaling procedures at each station.

On the other hand, it is also a desirable requirement to have some of the following practicalities in the climate change downscaling procedures. 1)

2) 3) 4) 5) 6)

Spatial, temporal or spatio-temporal domain of variability of the predictor. This corresponds to decision about the downscaling area (e.g. radius of influence) and time duration (day, month, season or year), What are the predictor GSM variables that are necessary for a particular predictand?, which is either precipitation or temperature or humidity in most of the cases, What type of downscaling procedure and methodology to be followed for the best results?, Calibration of the selected methodology by considering the local meteorological records and if possible satellite images, Model validation by meaningful interpretation of the final data with the local circumstances, If there are discrepancies then how to adjust the GCM variables to local observations and records?

DOWNSCALING DRAWBACKS Whatever downscaling procedure is chosen there are always some drawbacks and it is not possible to expect that one type of downscaling will be better that all others. It may be that some of the downscaling methods are more suitable for a location than others. For instance, mountainous regions require finer grids than flat areas such as deserts and plateau. Also the type of variable has dependence on the scale. In general, intermittent variables (such as precipitation) require finer mesh whereas continuous ones (such as temperature) may have coarser regional mesh. All downscaling methods have a set of assumptions and at times and places it is not easy to conform such assumptions to the existing local reality. It is, therefore, advised that prior to the application of any methodology and especially the use of software one should know the restrictive assumptions and interpret the final results accordingly. In dynamic downscaling procedures the atmospheric and meteorological phenomenon as well as boundary layer behavior within each grid is assumed to be homogeneous and isotropic. This indicates automatically the finer is the grid the better are the simulation results but in practical studies it is not possible to reduce the spatial mesh dimension in GCM less than a certain value, which is about 250–300 km presently. Theoretically it is possible to do so but practically the following drawbacks start to appear. 1)

2) 3)

The finer is the model mesh for simultaneous numerical solution of dynamic equations the more will be the time required for computation, which is not possible with the existing computer facilities. Increase in the resolution (finer mesh size) cause exponential increase in the time of computation as in Figure 4. Another problem with finer resolution is the uncertainty in the definition of boundary conditions, which require detailed information about the surface features, land use, population density, etc., In order to comply with finer scale solutions one needs to have dense observation network, which is not available for many parts of the world.



Mesh size

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Possible smallest mesh size ~ 30 km

Time

Figure 4. Mesh size versus time requirement

Under the light of the above mentioned difficulties one should try and make compromise between these difficulties and practicality, simplicity, cost and reliability. For the time being, many GCM scenario output generations are achieved at 250–300 km spacing of regular nodes. Another very significant difficulty is the basic fundamental understanding of dynamic equations and their validity for the study area especially in RegCM (small scale at about ∼30 km local GCM) approaches. There is no explicit spatial dependence or correlation function between the nodes but theoretically the dynamic equations take this point into view in an implicit manner by initial and boundary conditions. The major drawback of RegCM, which restricts its use in climate impact studies, is its complicated design and high computational cost. Moreover, RegCM is inflexible in the sense that expanding the region or moving to a slightly different region requires redoing the entire experiment (Crane and Hewitson, 1998). On the other hand, statistical downscaling methodologies are for finding mutual relationships between variables say CGM output variables and recorded data at some site. They have a set of restrictive assumptions, which cannot be satisfied with raw data in practical studies. Such assumptions are linearity, Gaussian distribution of the variables, homoscadasticity (constant variance) and independence of residuals. There are three implicit assumptions involved in statistical downscaling (Hewitson and Crane, 1996). For instance, the predictors (GCM results) are variables of relevance and are realistically modeled by the host GCM. Additionally, the empirical relationship is valid also under altered climatic conditions. Finally, the predictors employed fully represent the climate change signal. It is essential to sample meteorological and atmospheric events at a set of irregular measurement sites and then use quantitative methodologies for the identification of a set of parameters or a spatial map (pattern) for each variable, if necessary at different time durations (day, month, year), which can be then compared and classified into different categories (S¸en, 2009). Usually the pattern is invisible such as in the atmospheric sciences but based on the sampling, and thereafter, the data treatment with objective methodologies as well as personal expertise and intuition the general spatial features may be depicted in the form of maps such as the ones produced by GCMs and RegCM. In mapping procedure there are different geometrical functions that are used for the calculation of spatial weighted average. In all the methodologies so far classical weighting functions (mostly) are employed. GEOMETRIC WEIGHTING FUNCTIONS Operational objective analysis procedures help to interpolate in a practical way information from unevenly distributed observations to a uniformly distributed set of grid points or vice versa. The earliest studies started by Gilchrist and Cressman (1954) who reduced the domain of polynomial fitting to small areas surrounding each node with a parabola. Bergthhorsson and Döös (1955) proposed the basis of successive correction methods which did not rely only on interpretation to obtain grid point values but also a preliminary guess values are initially specified at the grid points. Cressman (1959) developed a number of further correction versions based on reported data falling within a specified distance R from each grid point. The value of R is decreased with successive scans and the resulting field of the latest scan is taken as the new approximation. Barnes (1964) summarized the development of a convergent weighted-averaging analysis scheme which can be used to obtain any desired amount of detail in the analysis of a set of


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W=1 1.0

W=

R 2 − r2 R2 + r 2

   2 r W = exp −4      R  

R2 − r 2  W = 2 2 R + r 

0

4

0

1

r R

Figure 5. Weighting functions randomly spaced data. The scheme is based on the supposition that the two-dimensional distribution of an atmospheric variable can be represented by the summation of an infinite number of independent waves, i.e., Fourier integral representation. A comparison of existing objective methods up to 1979 for sparse data is provided by Goodin, et. al. (1979). Their study indicated that fitting a second-degree polynomial to each sub-region triangular in the plane with each data point weighted according to its distance from the sub-region provides a compromise between accuracy and computational cost. Koch, et. al (1983) presented an extension of the Barnes method which is designed for an interactive computer scheme. Such a scheme allows real-time assessment both of the quality of the resulting analyses and of the impact of satellite-derived data upon various meteorological data sets. Both Cressman and Barnes methods include power parameter and radius of influence values, which are rather subjectively determined in the current meteorological practice. In the classical RegCM method Cressman procedure is used for regional predictions. In any optimum analysis technique, the main idea is that the estimation at any point is considered as a weighted average of the measured values at irregular sites. Hence, if there are i = 1, 2, . . . , n measurement sites with records Zi then the estimated site solar irradiation, ZE, can be calculated according to n

ZE =

∑WZ i=1 n

i

∑ Wi

i

(1)

i=1

which is most commonly used in different disciplines because of its explicit expression as the weighted average. Herein, each Wi corresponds to the weighting factor that is to be determined from a regional dependence function as will be explained in he next section. Weighting functions proposed by Cressman (1959), Gandin (1970) and Barnes (1964) also appear as sole functions of the distances between the sites only. Unfortunately, nvone of the weighting functions are event dependent, but they are suggested on the basis of the logical and geometrical conceptualizations of site configuration. Various geometrical weighting functions are shown in Figure 5.


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The weighting functions that are prepared on a rational and logical basis without consideration of regional data have the following major drawbacks. (a)

They do not take into consideration the natural variability of the regional variability features. For instance, in meteorology, Cressman (1959) weightings are given as,  R 2 − r2 i, E  W ( ri, E ) =  R 2 + ri2, E  0 

(b)

(c)

for ri, E ≤ R

(2)

for ri, E ≥ R

where W(ri, E) corresponds to Wi in Eq. (1); ri, E is the distance between the estimation point and other points; R is the radius of influence, which is determined subjectively by personal experience, Although weighting functions are considered universally applicable all over the world, they may show unreliable variability for small areas. For instance, within the same study area, neighboring sites may have quite different weighting functions, Geometric weighting functions cannot reflect the morphology, i.e., the regional variability of the phenomenon. They can only be considered as practical first approximation tools.

A generalized form of the Cressman model with an extra exponent parameter a is suggested as,  2 2 α  R − ri, E  W ( ri, E ) =  R 2 + ri2, E   0 

for ri, E ≤ R

(3)

for ri, E ≥ R

The inclusion of a has alleviated the aforesaid drawbacks to some extent but its determination still presents difficulties in practical applications. Another form of geometrical weighting function was proposed by Sasaki (1960) and Barnes (1964) as,   r 2  W ( ri, E ) = exp  −4  i, E     R    

(4)

In reality, it is expected that weighting functions should reflect the regional dependence behavior of the phenomenon. To this end, regional covariance and SV functions are among the early alternatives for the weighting functions that take into account the spatial correlation of the phenomenon considered. The former method requires a set of assumptions such as the Gaussian distribution of the regionalized variable. The latter technique, semivariogram (SV), does not always yield a clear pattern of regional correlation structure (S¸en, 1989). REGIONAL DEPENDENCE FUNCTION (RDF) None of the above mentioned weighting functions are data based and therefore their use includes systematic uncertainties and bias. Herein, real data based regional dependence function similar to Figure 5 are derived through the use of point cumulative semivariogram (PCSV) technique. For this purpose, the rainfall data have been selected from Istanbul City, Turkey, where there is an accelerating understanding about the plausible climate change effects on water resources in the context of socio-economic aspects. With the inherent scarcity of water in several parts of Istanbul and projected changes in climate for the coming decades, acute water shortages or critical droughts might be imminent in some parts of the city. It is shown by S¸en (1989, 2009) that a sample cumulative SV (CSV) or point CSV (PCSV) leads to a non-decreasing function with distance. The classical weighting functions appear as a non-increasing


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4000

• Observation

CSV (mm2)

VM

2000

••

• • •• • ••• • • • ••• • • • • ••

• •• ••

• •• ••• • •

•• •• •• • ••

•• • ••

••• •

•

• •

•• •• •• •

0 0

50

100 Distance (km)

150

RM

200

Figure 6. January CSV for Istanbul precipitation (S¸en, 1997) function with distance. It is, therefore, logical to execute the following steps in order to obtain a valid and standard weighting function from the sample CSV similar to the classical weighting functions. 1)

2)

3)

Depict on the sample CSV the maximum distance, RM, and corresponding sample CSV value, VM· RM corresponds to the distance between the two farthest station locations in any study area, (see Figure 6), Divide all the distances (CSV values) by RM (by VM) and the result appears as a scaled form of the sample CSV within limits of zero and one on both axis. This shows the change of dimensionless CSV with dimensionless distance, Subtraction of the dimensionless CSV values from the maximum value of one appears as a non-increasing function of the dimensionless distance as shown in Figure 7 which has similar pattern to all the classical weighting functions as explained in the previous section. This function is referred to as the RDF.

It is possible to conclude from this figure that CSV reaches almost horizontal value at large distances which means that after a certain distance there is no regional effect of one station on other stations’ rainfall amount (S¸en, 1997). This distance corresponds to R in Eqs. (2)–(4); Initially all the CSV’s have an intercept on the horizontal distance axis at about 2–3 km. This corresponds to almost the smallest distance between the stations. In order to explain the experimental CSV and thereof derived RDFs, the monthly rainfall amounts at a set of stations are considered, each with at least 30 years of records in the northwestern part of


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1 0.9

Observation

0.8

W=

R2 − r 2 R2 + r 2

0.7

RDF

0.6

 r2  W = exp −4 2  R

0.5 0.4 0.3 R2 − r 2  W= 2 2 R + r 

0.2

4

0.1 0

0

0.1

0.2

0.3

0.4 0.5 0.6 Dimensionless distance

0.7

0.8

0.9

1

Figure 7. January RDF for Istanbul precipitation (S¸en, 1997)

Turkey (S¸en, 1997). January CSV is presented in Figure 7 with corresponding classical and calculated RDF values in Figure 7. On the other hand, Figure 7 includes the geometric weighting functions already given in Figure 5 for the sake of comparison. Hence, the classical geometric weighting models do not have full justification for the whole of the meteorological phenomenon but they are good first approximations. They cannot be valid for the whole regional variability in any study area. In order to improve the representativeness of the precipitation regionalized variable estimations at sites, herein, an adaptive new technique is suggested, which does not only estimate the regional value at a site but also provides the number of the nearest sites that should be considered in the best possible regional estimation (S¸en, 2009). Accordingly, the radius of influence is defined as the distance between the estimation site and the far distant site within the adjacent sites that are considered in the regional estimation procedure. The following steps are necessary for the application of this adaptive procedure. 1)

2)

Take any site for cross-validation and apply Eq. (1) by considering the nearest site only. Such a selection is redundant and corresponds to the assumption that, if the nearest site measurement is considered only then the regional estimation will be equal to the same value. This means that in such a calculation the radius of influence is the minimum and equal to the distance between the estimation and the nearest sites, Consider now two of the nearest sites to the estimation site and apply the RDF weighting method according to Eq. (1). Consideration of two sites will increase the radius of influence as the distance between the estimation and the next nearest site and the estimation value will assume weighted value of the two nearest sites. Since, the weights and measurements are positive numbers; the estimated value will be between the measurements at the two nearest sites. There will be a squared estimation error as the square of the difference between measured and estimated values,


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50 60

0 0

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150

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200 Easting 100

250

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350

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200

Figure 8. Radius of influence map (m)

3)

Repeat the same procedure now with three nearest stations and calculate the square error likewise. Subsequently, it is possible to continue with 4, 5, . . . , (n–1) nearest sites consequently, and for each case to calculate corresponding square error. The first one with the least square error yields the number of nearest sites for the best regional Fe % concentration estimation. The distance of the farthest site in such a situation corresponds to the radius of influence. Application of this procedure yields the estimation values, number of the nearest sites with the minimum squared error and the radius of influence. It is possible to construct equal radii regional map as in Figure 8.

From this map one can know the relevant radius of influence for any desired point within the study area. Once, this radius is determined then a circle with the center at the prediction point is drawn. The measurement sites within this circle are taken into consideration in the application of Eq. (1) for regional estimation through the RDF weights. Although reliable short range operational forecasts of seasonal temperature and precipitation can be achieved by understanding the climate system, it is rather difficult to make longer range predictions at spatio-temporal scales. Such predictions have already been successfully obtained the Climate Prediction Center (CPC) of the U.S. National Centers for Environmental Prediction (Barnston et al. 1994) and the


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International Research Institute (IRI) for Climate Prediction. Comparison of past seasonal forecasts with corresponding observed seasonal outcomes has demonstrated real and potentially useful information content (Wilks 2000a; Wilks and Godfrey 2000, 2002), but the temporally aggregated nature of the forecast quantities may be difficult for some decision makers to incorporate into their operations. CONCLUSIONS Climate change modeling in global scale and its impacts in local scale are one of the most socioeconomical issues in future planning of any country and central as well as local administrations in the 21st century. The general circulation (climate) models (GCMs) help to provide global data at a set of nodes based on a global grid net where the distance between two nodes is rather course as about 300 km where local climate effect assessments require smaller resolutions if possible down to meter. Such a requirement necessitates development of techniques that assume input data from GCM outputs and provides local estimations. The techniques that appear in open literature can be categorized into three classes, namely, dynamic, statistical and hybrid downscaling methodologies. In this paper, existing methods are explained with emphasis on their drawbacks and then a new approach is proposed in terms of point cumulative semivariogram leading to regional dependence function (RDF) and its application steps are shown leading to equal radii map and then onwards estimation at any desired point by use of this RDF. REFERENCES Arnell, N.W., Hudson, D.A., Jones, R.G., 2003. Climate change scenarios from a regional climate model: Estimating change in runoff in southern Africa. Journal of Geophysical Research – Atmospheres 108 (D16), AR 4519. Barnes, S. L., 1964. A technique for maximizing details in numerical weather map analysis. J. Appl. Meteor., 3, 396–409. Barnston, A.G., H.M. van den Dool, S.E. Zebiak, T.P. Barnett, M. Ji, D.R. Rodenhuis, M.A. Cane, A. Leetmaa, N.E. Graham, C.F. Ropelewski, V.E. Kousky, E. A. O’Lenic and R.E. Livezey, 1994: Long-lead seasonal forecasts-Where do we stand? Bull. Amer. Meteor. Soc., 75, 2097–2114. Bergthorsson, P., and Döös, B. R., 1955. Numerical weather map analysis. Tellus, 7, 329–340. Bouraoui, F., Vachaud, G., Li, L.Z.X., Le Treut, H., Chen, T., 1999. Evaluation of the impact of climate changes on water storage and groundwater recharge at the watershed scale. Climate Dynamics 15, 153–161. Buma, J., Dehn, M., 2000. Impact of climate change on a landslide in South East France, simulated using different GCM scenarios and downscaling methods for local precipitation. Climate Research 15 (1), 69–81. Cannon, A.J., Whitfield, P.H., 2002. Downscaling recent streamflow conditions in British Columbia, Canada using ensemble neural network models. Journal of Hydrology 259 (1), 136–151. Cavazos, T., 1997. Downscaling large-scale circulation to local winter rainfall in north-eastern Mexico. International Journal of Climatology 17 (10), 1069–1082. Cortes, C., Vapnik, V., 1995. Support vector networks. Machine Learning 20, 273–297. Crane, R.G., Hewitson, B.C., 1998. Doubled CO2 precipitation changes for the Susquehanna Basin: Down-Scaling from the Genesis General Circulation Model. International Journal of Climatology 18, 65–76. Crane, R.G., Yarnal, B., Barron, E.J., Hewitson, B., 2002. Scale interactions and regional climate: Examples from the Susquehanna River Basin. Human and Ecological Risk Assessment 8 (1), 147–158. Cressman, G. P., 1959. An operational objective analysis system. Mon. Wea. Rev., 87, 367–374. Cristianini, N., Shawe-Taylor, J., 2000. An Introduction to Support Vector Machines and other Kernelbased Learning Methods. Cambridge University Press, Cambridge.


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